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2x+2=1/2x+7
We move all terms to the left:
2x+2-(1/2x+7)=0
Domain of the equation: 2x+7)!=0We get rid of parentheses
x∈R
2x-1/2x-7+2=0
We multiply all the terms by the denominator
2x*2x-7*2x+2*2x-1=0
Wy multiply elements
4x^2-14x+4x-1=0
We add all the numbers together, and all the variables
4x^2-10x-1=0
a = 4; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·4·(-1)
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{29}}{2*4}=\frac{10-2\sqrt{29}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{29}}{2*4}=\frac{10+2\sqrt{29}}{8} $
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